- #1
LagrangeEuler
- 717
- 20
I don't understand this idea. For example we have cubic crystal which has a lot of unit cells. We define spin variable of center of cell like [tex]S_c[/tex]. And spin variable of nearest neighbour cells with [tex]S_{c+r}[/tex]. So the cell hamiltonian is
[tex]\hat{H}=\frac{1}{2}J\sum_{c}\sum_{r}(S_c-S_{c+r})^2+\sum_cU(S_c^2)[/tex]
This model is simulation of uniaxial feromagnet.
I have three question:
1. What's the difference between Ising model and 1d Heisenberg model?
2. Why this model is better than Ising model with no cells? Where we have just spins which interract.
[tex]\hat{H}=-J\sum_iS_{i}S_{i+1}[/tex]
3. What [tex]\sum_cU(S_c^2)[/tex] means physically?
Tnx.
[tex]\hat{H}=\frac{1}{2}J\sum_{c}\sum_{r}(S_c-S_{c+r})^2+\sum_cU(S_c^2)[/tex]
This model is simulation of uniaxial feromagnet.
I have three question:
1. What's the difference between Ising model and 1d Heisenberg model?
2. Why this model is better than Ising model with no cells? Where we have just spins which interract.
[tex]\hat{H}=-J\sum_iS_{i}S_{i+1}[/tex]
3. What [tex]\sum_cU(S_c^2)[/tex] means physically?
Tnx.